HartmutHolzwart wrote:Congratulations! This is really progress! How did you search for this? Can we expect more?

The new c/5 orthogonal wickstretcher was found by doing a width-17 reverse gfind-pt search starting from the known wick (following these instructions). obviously no width-17 symmetric stretcher exists, but I checked the partial results every once in a while, and I eventually found one that could be supported by two domino sparks.

The c/6 orthogonal tagalong was found with with WLS after noticing the following reaction in a modified gfind search:

Here's a question: is it possible for a ship to exceed c/2? Yes, I know that the speed of light cannot be attained (a vertical line does, but is not a spaceship), but could a ship with a velocity of just sliiiightly over c/2 exist? Something really barely faster like 9c/16 or 1337c/2673?

And what would the slowest possible spaceship? This c/5648 thing exists, but only within a different rule:

muzik wrote:Here's a question: is it possible for a ship to exceed c/2?...

It has been proven impossible for anything inside the game of life to exceed c/2 in speed, but in B2 rules it's theoretically possible.

muzik wrote:And what would [be] the slowest possible spaceship?...

There is no slowest possible spaceship, spaceships can be infinitely slow in the game of life. One can trivially modify the Gemini spaceship so as to make its construction process slightly slower. However, we have yet to find a spaceship that can be adjusted in this manner in another rule.

There is no slowest possible spaceship, spaceships can be infinitely slow in the game of life. One can trivially modify the Gemini spaceship so as to make its construction process slightly slower. However, we have yet to find a spaceship that can be adjusted in this manner in another rule.

well, to rephrase that: What would the slowest orthogonal spaceship be?

Sokwe wrote:If a spaceship with velocity (m,n)c/p exists in Conway's Game of Life (where m and n are the vertical and horizontal displacements and p is the period), then we must have m + n <= p/2.

Wait, what?

Explain please?

Nathaniel wrote a nice article about this here. It only shows the c/4 diagonal and c/2 orthogonal speed limits, but this method can be extended to show the claim I made above. I encourage you to think about why this is.

muzik wrote:well, to rephrase that: What would the slowest orthogonal spaceship be?

There is no "slowest orthogonal spaceship". For any speed in any direction, we can always build a spaceship that is slower than that speed. All we need to do is make a constructor based spaceship that displaces itself by a fixed amount and then performs some time-wasting activity to increase the period as much as we want. As I recall, ge

c/2 is the orthogonal speed limit, at least for a spaceship propagating in empty space. There are ways to make faster propagation within a fixed background, see for example the discussions of signals or Gabriel Nivasch's discussion of lightspeed signals here. But to be called a spaceship it needs to have emptiness in front of and behind it.

Regarding the lower: isn't the Waterbear exactly what you said: "a spaceship that consists of multiple other spaceships slowing each other down via some strange reaction"?

c/2 is the orthogonal speed limit, at least for a spaceship propagating in empty space. There are ways to make faster propagation within a fixed background, see for example the discussions of signals or Gabriel Nivasch's discussion of lightspeed signals here. But to be called a spaceship it needs to have emptiness in front of and behind it.

Regarding the lower: isn't the Waterbear exactly what you said: "a spaceship that consists of multiple other spaceships slowing each other down via some strange reaction"?

Indeed, but it's not an orthogonal spaceship. Those are my main interests.

muzik wrote:Indeed, but it's not an orthogonal spaceship. Those are my main interests.

Well then you should look at the Engineless Caterpillar thread, which was an attempt to make a recipe for any sufficiently slow orthogonal spaceship using that sort of process. I don't know why it has been inactive lately..

Sorry, I started writing a sentence, but I decided against it. Unfortunately, I forgot to delete what I had written. What I was going to say was that, from what I recall, the original Gemini design allowed for the construction of arbitrarily slow orthogonal spaceships.

Sorry, I started writing a sentence, but I decided against it. Unfortunately, I forgot to delete what I had written. What I was going to say was that, from what I recall, the original Gemini design allowed for the construction of arbitrarily slow orthogonal spaceships.

That makes sense. What's the fastest speed you can make one of those construct at?

It depends on how you define "spaceship". Typically, spaceships are defined to have some non-zero displacement.

muzik wrote:What's the fastest speed you can make one of those [Gemini] construct at?

For the original design, I think the speed of a ship with a velocity (m,n)c/p is limited by 4*m+576*(m+n)/2 < p and m > n > 0.

Disclaimer: the following analysis is not guaranteed to be correct.

Consider the original Gemini design travelling up and left (the same orientation that the original Gemini was posted in). Let m be the vertical (upward) displacement and let n be the horizontal (leftward) displacement. In the original Gemini there are two independent construction arms. The circuitry for each construction arm has a repeat time of 576 generations. That is, one "cycle" of the circuitry takes 576 generations. During each cycle, the ends of each construction arm can be pushed diagonally by one cell. After a push of either of these construction arms, it takes an extra 4 generations for the next set of gliders to reach the end of the construction arm.

Let A be the number of pushes in the up-left direction, and let B be the number of pushes in the up-right direction. Notice that m=A+B and n=A-B. Notice also that A >= B since we assumed the ship was traveling left. Then the total period of the Geminoid is

On a similar note, it is theoretically possible to produce any rational spaceship velocity with 'absolute speed' (ie. the speed compared to the fastest possible information transfer with the same slope) less than or equal to c/2, if it is possible to slow-salvo construct a c/2 puffer for the 2c/3 blinker fuse. c/2 orthogonal and c/4 diagonal have explicit examples, and any slower speed could be constructed by sending out such a puffer above, ignite it, and shoot *WSS salvos at it. This also assumes that slow *WSS salvos are capable of universal construction though, which is likely.

Sokwe wrote:If a spaceship with velocity (m,n)c/p exists in Conway's Game of Life (where m and n are the vertical and horizontal displacements and p is the period), then we must have m + n <= p/2.

Wait, what?

Explain please?

Nathaniel wrote a nice article about this here. It only shows the c/4 diagonal and c/2 orthogonal speed limits, but this method can be extended to show the claim I made above. I encourage you to think about why this is.

To add to that, in Life, no pattern can ever "grow out" to the next half-diagonal in two consecutive generations (for details, see Nathaniel's article). It helps to think of a diagonal line of slope -1 that lies above a pattern and moves upward one cell every two generations, and the pattern can never cross this line. The c/4 diagonal, c/2 orthogonal, and m + n <= p/2 speed limits immediately follow from this.

Other cellular automata may have different speed limits. A B3 rule with S4 or S5 may have diagonal speed up to c/3, and orthogonal speed is still limited to c/2 (in this case, the bounding line has slope -1/2 and moves upward one cell every two generations, or alternatively moves rightward one cell every generation). B2 rules have max c/2 diagonal and c orthogonal, and B1 rules have growth of c in every direction (of course, no spaceships).

Wait -- I can see how to get any speed strictly less than c/2 (by l_1 metric), but how do you handle the equality case? In particular, I don't think you've proved that there exists a (2, 1)c/6 spaceship.

What do you do with ill crystallographers? Take them to the mono-clinic!

I like the new thread. It is more convenient, as I have a variety of stuff.

I did some more 4c/10 glide symmetric searches. At width 17 there are no period 10 ships with a period 10 front row. There are many period 5 tags to sift through in hopes of finding period 10 extensions. I checked a lot of the period 5 tags, though certainly not all of them. I was hoping to find a large period 10 section, but none were to be had. I did find the following period 10 glide symmetric ship. It actually has a width 19 spark, as knight3 only restricts the width on 2 of the 5 phases for this search.

Using knight2 I did a variety of 2c/8 glide symmetric searches. Again, I was hoping to find a pure period 8 ship but none have shown up. My width 18 search for ships with a period 8 front row is nearing completion and it appears that it will end with no ships found. I did notice a partial that had an even symmetric period 4 end. It took me an hour to set up and ten minutes to run to find a width 24 completion.

I also did a 2c/6 width 21 glide symmetric search with an asymmetric period 6 front row first phase. I know that Josh Ball did a similar search and I have included his results in the following collection. Josh's ships are the fourth and fifth on the first row. All 2c/6 width 21 glide symmetric ships have either Josh's front end or my front end. The third ship on the first row I found previously and finished it off at period 3. The second ship on the first row is probably the minimum length for this type of ship. It is length 51. I will know for sure in the next few days, as the last remaining alternatives are currently at length 46. The width 21 search tree gets very wide at that length with variations on ships in the second row. At about length 28 Josh's front end necks down to ~width 13. I did a width 15 exploratory extension starting at row 28 and the results of that search are on the second row. Ships 1 2 4 5 6 7 on the second row all have backends that have been previously posted and are in jslife. I haven't seen the other backends.

I have made several updates to knight2 and will be posting updated code on the knight2 thread on the scripts page in the next few days.

One thing that I have noticed in doing these higher period searches is that increasing the search width is providing very little benefit or encouragement in finding spaceships. This was particularly noticeable in the period 8 and period 10 searches that I did.

calcyman wrote:Wait -- I can see how to get any speed strictly less than c/2 (by l_1 metric), but how do you handle the equality case? In particular, I don't think you've proved that there exists a (2, 1)c/6 spaceship.

I made a mistake, the equality shouldn't be there. And it probably isn't even true, since none of those velocities with velocity (x,y)c/2(x+y) are achievable by a ship that moves itself by universal construction, and the problem of determining if a spaceship exists at that velocity for any arbitrary choice of x and y is probably undecidable.